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Full text of "Mathematical And Physical Papers - Iii"

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Observations on the preceding results.
80.    There is one law relating to internal dispersion which appears to be universal, namely, that when the refrangibiiity of light is  changed  by dispersion  it is  always lowered.    I have examined a great many media besides those which have been mentioned, and I have not met with a single exception to this rule.    Once or twice, in observing by the fourth method, there appeared at first sight to be some dispersed light produced when the  small  lens  was  placed  beyond the extreme red.    But on further examination I satisfied myself that this was due merely to the light scattered at the surfaces of the large prisms and lens, which thus acted the part of a self-luminous body, emitting a light of sufficient intensity to affect a very sensitive medium.
81.    Consider light of given refrangibiiity incident on a given medium.    Let some numerical quantity be taken for a measure of the refrangibiiity, suppose the refractive index in some standard substance.    Let the refrangibilities of the incident and dispersed light be laid down along a straight line AX (fig. 2) taken for the axis of abscissae; let AM represent the refrangibiiity of the incident light, and draw a curve of which the ordinates shall represent the intensities of the component parts of the truly dispersed beam. According to the law above stated, no part of the curve is ever found to the right of the point M; but in other respects its form admits of great latitude.    Sometimes the curve progresses with tolerable uniformity, sometimes it presents several maxima and minima, or even appears to consist of distinct portions.    Sometimes it is well separated from M, as in fig. 2;   sometimes  it approaches so near to M that the most refrangible portion of the truly dispersed beam is confounded with the beam due to false dispersion.
82.    Let f(oc) be the ordinate of the curve corresponding to the abscissa x, a the abscissa of the point M.    Since f(x) is equal to zero when x exceeds a, the curve must reach the axis at the point M at latest, unless we suppose the function capable of altering abruptly, as is represented in fig. 3.    I do not think that such an abrupt alteration, properly understood, is necessarily in contra-